Magic number

Magic number, in physics, in the shell models of both atomic and nuclear structure, any of a series of numbers that connote stable structure.

The magic numbers for atoms are 2, 10, 18, 36, 54, and 86, corresponding to the total number of electrons in filled electron shells. (Electrons within a shell have very similar energies and are at similar distances from the nucleus.) In the chemical elements of atomic number 17 to 19, for example, the chloride ion (Cl−), the argon atom (Ar), and the potassium ion (K+) have 18 electrons in closed-shell configurations and are chemically quite stable. The number of electrons present in the neutral atoms constituting the relatively unreactive noble gases exactly correspond to the atomic magic numbers.

The magic numbers for nuclei are 2, 8, 20, 28, 50, 82, and 126. Thus, tin (atomic number 50), with 50 protons in its nucleus, has 10 stable isotopes, whereas indium (atomic number 49) and antimony (atomic number 51) have only 2 stable isotopes apiece. The doubly magic alpha particle, or helium-4 nucleus, composed of two protons and two neutrons, is very stable. In nuclei, this increased stability occurs when there is a large energy gap between a series of filled energy levels and the next level, which is empty. Such large gaps are said to separate shells, although these shells are not as clearly linked to the spatial structure of the nucleus as electron shells are to their orbits.

Learn More in these related articles:

...These peaks are associated with nuclei containing 50, 82, or 126 neutrons; the theory of nuclear structure predicts that these nuclei should be particularly stable, and these numbers are known as “magic” numbers.

...or neutrons complete a nuclear shell (that is, arrive at certain fixed values), the nucleus is exceptionally stable; the number of protons or neutrons required to complete a shell is called a magic number. One particular magic number—82 for neutrons—occurs in the lanthanide series.

In the preceding section, the overall trends of nuclear binding energies were described in terms of a charged-liquid-drop model. Yet there were noted periodic binding-energy irregularities at the magic numbers. The periodic occurrence of magic numbers of extra stability is strongly analogous to the extra electronic stabilities occurring at the atomic numbers of the noble-gas atoms. The...